On Information (pseudo) Metric
This provides a theoretical refinement of information geometry for researchers in statistics and machine learning, but appears incremental.
The paper revisits the information metric, showing it is a pseudo metric on manifolds of observables rather than probability laws, and characterizes geodesics with boundaries and conditional independence. It computes this metric on the Diabetes dataset using the infotopo package.
This short note revisit information metric, underlining that it is a pseudo metric on manifolds of observables (random variables), rather than as usual on probability laws. Geodesics are characterized in terms of their boundaries and conditional independence condition. Pythagorean theorem is given, providing in special case potentially interesting natural integer triplets. This metric is computed for illustration on Diabetes dataset using infotopo package.